Multiscale reconstruction for computational spectral imaging

Abstract

In this work we develop a spectral imaging system and associated reconstruction methods that have been designed to exploit the theory of compressive sensing. Recent work in this emerging field indicates that when the signal of interest is very sparse (i.e. zero-valued at most locations) or highly compressible in some basis, relatively few incoherent observations are necessary to reconstruct the most significant non-zero signal components. Conventionally, spectral imaging systems measure complete data cubes and are subject to performance limiting tradeoffs between spectral and spatial resolution. We achieve single-shot full 3D data cube estimates by using compressed sensing reconstruction methods to process observations collected using an innovative, real-time, dual-disperser spectral imager. The physical system contains a transmissive coding element located between a pair of matched dispersers, so that each pixel measurement is the coded projection of the spectrum in the corresponding spatial location in the spectral data cube. Using a novel multiscale representation of the spectral image data cube, we are able to accurately reconstruct 256 × 256 × 15 spectral image cubes using just 256 × 256 measurements.Keywords: wavelets, compressed sensing, hyperspectral imaging COMPRESSIVE SPECTRAL IMAGINGSpectral imaging is a highly effective tool in a variety of scientific and engineering contexts because of the information it implicitly encodes about the nature of the materials being imaged. While traditional digital imaging techniques produce images with scalar values associated with each spatial pixel location, in spectral images these scalar values are replaced with a vector containing the spectral information from that spatial location. The resulting data is therefore three-dimensional (two spatial dimensions and one spectral dimension). Spectral information can be vital for tasks such as monitoring the health of a forest ecosystem [1,2], increasing our understanding of solar physics [3], or examining tissue and organisms used to study cellular dynamics [4, 5].Despite its potential, however, many modern spectral imagers face a limiting tradeoff between spatial and spectral resolution, with the total number of voxels measured constrained by the size of the detector array. This constraint limits the utility and cost-effectiveness of spectral imaging for many applications. Furthermore, straightforward application of traditional spectroscopic techniques to spectral imaging proves problematic. The simplest spectral imager forms combine either a pushbroom (linear scanning) or tomographic (rotational scanning) front-end with a traditional slit-based dispersive spectrometer. Unfortunately, in many of the most interesting applications (most notably biophotonics) the sources are often both spatially-incoherent and weak. Spatially-incoherent sources present a significant challenge to slit-based dispersive spectrometers, and extremely poor photon collection efficiency is the result. When the source is also weak, the abso...

Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging

“…This relationship can be directed to the recent development of compressive sensing [42][43][44][45]. Further investigations along this line are highly desired.…”

Spatio-spectral uniform multi-frame coded apertures for compressive spectral imaging

“…Traditionally, the coded aperture entries are obtained as realizations of a Bernoulli random variable, Hadamard matrices, S matrices [1], [4] and, cyclic S-matrices obtained as cyclic permutations of a codeword [5]. These types of random codes however, do not fully exploit the richness of compressed sensing theory.…”

Emerging theories and technologies on computational imaging

“…Based on this basic principle, researchers have designed different spectrum sampling systems, with various optical implementations and system structures. We can classify them into branches according to their sampling and reconstruction strategies, including computed tomography (Descour and Dereniak, 1995), interferometry (Chao et al, 2005), coded aperture (Willett et al, 2007), and hybrid-camera systems (Ma et al, 2014). In addition, compressive sensing has recently drawn much attention in the computational imaging field.…”